mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-29 05:51:10 +00:00
366 lines
12 KiB
C
366 lines
12 KiB
C
/* Software floating-point emulation.
|
|
Basic one-word fraction declaration and manipulation.
|
|
Copyright (C) 1997-2023 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
|
|
The GNU C Library is free software; you can redistribute it and/or
|
|
modify it under the terms of the GNU Lesser General Public
|
|
License as published by the Free Software Foundation; either
|
|
version 2.1 of the License, or (at your option) any later version.
|
|
|
|
In addition to the permissions in the GNU Lesser General Public
|
|
License, the Free Software Foundation gives you unlimited
|
|
permission to link the compiled version of this file into
|
|
combinations with other programs, and to distribute those
|
|
combinations without any restriction coming from the use of this
|
|
file. (The Lesser General Public License restrictions do apply in
|
|
other respects; for example, they cover modification of the file,
|
|
and distribution when not linked into a combine executable.)
|
|
|
|
The GNU C Library is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
Lesser General Public License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public
|
|
License along with the GNU C Library; if not, see
|
|
<https://www.gnu.org/licenses/>. */
|
|
|
|
#ifndef SOFT_FP_OP_1_H
|
|
#define SOFT_FP_OP_1_H 1
|
|
|
|
#define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f _FP_ZERO_INIT
|
|
#define _FP_FRAC_COPY_1(D, S) (D##_f = S##_f)
|
|
#define _FP_FRAC_SET_1(X, I) (X##_f = I)
|
|
#define _FP_FRAC_HIGH_1(X) (X##_f)
|
|
#define _FP_FRAC_LOW_1(X) (X##_f)
|
|
#define _FP_FRAC_WORD_1(X, w) (X##_f)
|
|
|
|
#define _FP_FRAC_ADDI_1(X, I) (X##_f += I)
|
|
#define _FP_FRAC_SLL_1(X, N) \
|
|
do \
|
|
{ \
|
|
if (__builtin_constant_p (N) && (N) == 1) \
|
|
X##_f += X##_f; \
|
|
else \
|
|
X##_f <<= (N); \
|
|
} \
|
|
while (0)
|
|
#define _FP_FRAC_SRL_1(X, N) (X##_f >>= N)
|
|
|
|
/* Right shift with sticky-lsb. */
|
|
#define _FP_FRAC_SRST_1(X, S, N, sz) __FP_FRAC_SRST_1 (X##_f, S, (N), (sz))
|
|
#define _FP_FRAC_SRS_1(X, N, sz) __FP_FRAC_SRS_1 (X##_f, (N), (sz))
|
|
|
|
#define __FP_FRAC_SRST_1(X, S, N, sz) \
|
|
do \
|
|
{ \
|
|
S = (__builtin_constant_p (N) && (N) == 1 \
|
|
? X & 1 \
|
|
: (X << (_FP_W_TYPE_SIZE - (N))) != 0); \
|
|
X = X >> (N); \
|
|
} \
|
|
while (0)
|
|
|
|
#define __FP_FRAC_SRS_1(X, N, sz) \
|
|
(X = (X >> (N) | (__builtin_constant_p (N) && (N) == 1 \
|
|
? X & 1 \
|
|
: (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
|
|
|
|
#define _FP_FRAC_ADD_1(R, X, Y) (R##_f = X##_f + Y##_f)
|
|
#define _FP_FRAC_SUB_1(R, X, Y) (R##_f = X##_f - Y##_f)
|
|
#define _FP_FRAC_DEC_1(X, Y) (X##_f -= Y##_f)
|
|
#define _FP_FRAC_CLZ_1(z, X) __FP_CLZ ((z), X##_f)
|
|
|
|
/* Predicates. */
|
|
#define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE) X##_f < 0)
|
|
#define _FP_FRAC_ZEROP_1(X) (X##_f == 0)
|
|
#define _FP_FRAC_OVERP_1(fs, X) (X##_f & _FP_OVERFLOW_##fs)
|
|
#define _FP_FRAC_CLEAR_OVERP_1(fs, X) (X##_f &= ~_FP_OVERFLOW_##fs)
|
|
#define _FP_FRAC_HIGHBIT_DW_1(fs, X) (X##_f & _FP_HIGHBIT_DW_##fs)
|
|
#define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f)
|
|
#define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f)
|
|
#define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f)
|
|
|
|
#define _FP_ZEROFRAC_1 0
|
|
#define _FP_MINFRAC_1 1
|
|
#define _FP_MAXFRAC_1 (~(_FP_WS_TYPE) 0)
|
|
|
|
/* Unpack the raw bits of a native fp value. Do not classify or
|
|
normalize the data. */
|
|
|
|
#define _FP_UNPACK_RAW_1(fs, X, val) \
|
|
do \
|
|
{ \
|
|
union _FP_UNION_##fs _FP_UNPACK_RAW_1_flo; \
|
|
_FP_UNPACK_RAW_1_flo.flt = (val); \
|
|
\
|
|
X##_f = _FP_UNPACK_RAW_1_flo.bits.frac; \
|
|
X##_e = _FP_UNPACK_RAW_1_flo.bits.exp; \
|
|
X##_s = _FP_UNPACK_RAW_1_flo.bits.sign; \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_UNPACK_RAW_1_P(fs, X, val) \
|
|
do \
|
|
{ \
|
|
union _FP_UNION_##fs *_FP_UNPACK_RAW_1_P_flo \
|
|
= (union _FP_UNION_##fs *) (val); \
|
|
\
|
|
X##_f = _FP_UNPACK_RAW_1_P_flo->bits.frac; \
|
|
X##_e = _FP_UNPACK_RAW_1_P_flo->bits.exp; \
|
|
X##_s = _FP_UNPACK_RAW_1_P_flo->bits.sign; \
|
|
} \
|
|
while (0)
|
|
|
|
/* Repack the raw bits of a native fp value. */
|
|
|
|
#define _FP_PACK_RAW_1(fs, val, X) \
|
|
do \
|
|
{ \
|
|
union _FP_UNION_##fs _FP_PACK_RAW_1_flo; \
|
|
\
|
|
_FP_PACK_RAW_1_flo.bits.frac = X##_f; \
|
|
_FP_PACK_RAW_1_flo.bits.exp = X##_e; \
|
|
_FP_PACK_RAW_1_flo.bits.sign = X##_s; \
|
|
\
|
|
(val) = _FP_PACK_RAW_1_flo.flt; \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_PACK_RAW_1_P(fs, val, X) \
|
|
do \
|
|
{ \
|
|
union _FP_UNION_##fs *_FP_PACK_RAW_1_P_flo \
|
|
= (union _FP_UNION_##fs *) (val); \
|
|
\
|
|
_FP_PACK_RAW_1_P_flo->bits.frac = X##_f; \
|
|
_FP_PACK_RAW_1_P_flo->bits.exp = X##_e; \
|
|
_FP_PACK_RAW_1_P_flo->bits.sign = X##_s; \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Multiplication algorithms: */
|
|
|
|
/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
|
|
multiplication immediately. */
|
|
|
|
#define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y) \
|
|
do \
|
|
{ \
|
|
R##_f = X##_f * Y##_f; \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \
|
|
do \
|
|
{ \
|
|
_FP_MUL_MEAT_DW_1_imm ((wfracbits), R, X, Y); \
|
|
/* Normalize since we know where the msb of the multiplicands \
|
|
were (bit B), we know that the msb of the of the product is \
|
|
at either 2B or 2B-1. */ \
|
|
_FP_FRAC_SRS_1 (R, (wfracbits)-1, 2*(wfracbits)); \
|
|
} \
|
|
while (0)
|
|
|
|
/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
|
|
|
|
#define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit) \
|
|
do \
|
|
{ \
|
|
doit (R##_f1, R##_f0, X##_f, Y##_f); \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \
|
|
do \
|
|
{ \
|
|
_FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_wide_Z); \
|
|
_FP_MUL_MEAT_DW_1_wide ((wfracbits), _FP_MUL_MEAT_1_wide_Z, \
|
|
X, Y, doit); \
|
|
/* Normalize since we know where the msb of the multiplicands \
|
|
were (bit B), we know that the msb of the of the product is \
|
|
at either 2B or 2B-1. */ \
|
|
_FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_wide_Z, (wfracbits)-1, \
|
|
2*(wfracbits)); \
|
|
R##_f = _FP_MUL_MEAT_1_wide_Z_f0; \
|
|
} \
|
|
while (0)
|
|
|
|
/* Finally, a simple widening multiply algorithm. What fun! */
|
|
|
|
#define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y) \
|
|
do \
|
|
{ \
|
|
_FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_xh, _FP_MUL_MEAT_DW_1_hard_xl; \
|
|
_FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_yh, _FP_MUL_MEAT_DW_1_hard_yl; \
|
|
_FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_1_hard_a); \
|
|
\
|
|
/* Split the words in half. */ \
|
|
_FP_MUL_MEAT_DW_1_hard_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \
|
|
_FP_MUL_MEAT_DW_1_hard_xl \
|
|
= X##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
|
|
_FP_MUL_MEAT_DW_1_hard_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \
|
|
_FP_MUL_MEAT_DW_1_hard_yl \
|
|
= Y##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
|
|
\
|
|
/* Multiply the pieces. */ \
|
|
R##_f0 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yl; \
|
|
_FP_MUL_MEAT_DW_1_hard_a_f0 \
|
|
= _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yl; \
|
|
_FP_MUL_MEAT_DW_1_hard_a_f1 \
|
|
= _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yh; \
|
|
R##_f1 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yh; \
|
|
\
|
|
/* Reassemble into two full words. */ \
|
|
if ((_FP_MUL_MEAT_DW_1_hard_a_f0 += _FP_MUL_MEAT_DW_1_hard_a_f1) \
|
|
< _FP_MUL_MEAT_DW_1_hard_a_f1) \
|
|
R##_f1 += (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2); \
|
|
_FP_MUL_MEAT_DW_1_hard_a_f1 \
|
|
= _FP_MUL_MEAT_DW_1_hard_a_f0 >> (_FP_W_TYPE_SIZE/2); \
|
|
_FP_MUL_MEAT_DW_1_hard_a_f0 \
|
|
= _FP_MUL_MEAT_DW_1_hard_a_f0 << (_FP_W_TYPE_SIZE/2); \
|
|
_FP_FRAC_ADD_2 (R, R, _FP_MUL_MEAT_DW_1_hard_a); \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \
|
|
do \
|
|
{ \
|
|
_FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_hard_z); \
|
|
_FP_MUL_MEAT_DW_1_hard ((wfracbits), \
|
|
_FP_MUL_MEAT_1_hard_z, X, Y); \
|
|
\
|
|
/* Normalize. */ \
|
|
_FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_hard_z, \
|
|
(wfracbits) - 1, 2*(wfracbits)); \
|
|
R##_f = _FP_MUL_MEAT_1_hard_z_f0; \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Division algorithms: */
|
|
|
|
/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
|
|
division immediately. Give this macro either _FP_DIV_HELP_imm for
|
|
C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you
|
|
choose will depend on what the compiler does with divrem4. */
|
|
|
|
#define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \
|
|
do \
|
|
{ \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r; \
|
|
X##_f <<= (X##_f < Y##_f \
|
|
? R##_e--, _FP_WFRACBITS_##fs \
|
|
: _FP_WFRACBITS_##fs - 1); \
|
|
doit (_FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r, X##_f, Y##_f); \
|
|
R##_f = _FP_DIV_MEAT_1_imm_q | (_FP_DIV_MEAT_1_imm_r != 0); \
|
|
} \
|
|
while (0)
|
|
|
|
/* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
|
|
that may be useful in this situation. This first is for a primitive
|
|
that requires normalization, the second for one that does not. Look
|
|
for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */
|
|
|
|
#define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \
|
|
do \
|
|
{ \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nh; \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nl; \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_q; \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_r; \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_y; \
|
|
\
|
|
/* Normalize Y -- i.e. make the most significant bit set. */ \
|
|
_FP_DIV_MEAT_1_udiv_norm_y = Y##_f << _FP_WFRACXBITS_##fs; \
|
|
\
|
|
/* Shift X op correspondingly high, that is, up one full word. */ \
|
|
if (X##_f < Y##_f) \
|
|
{ \
|
|
R##_e--; \
|
|
_FP_DIV_MEAT_1_udiv_norm_nl = 0; \
|
|
_FP_DIV_MEAT_1_udiv_norm_nh = X##_f; \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_DIV_MEAT_1_udiv_norm_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \
|
|
_FP_DIV_MEAT_1_udiv_norm_nh = X##_f >> 1; \
|
|
} \
|
|
\
|
|
udiv_qrnnd (_FP_DIV_MEAT_1_udiv_norm_q, \
|
|
_FP_DIV_MEAT_1_udiv_norm_r, \
|
|
_FP_DIV_MEAT_1_udiv_norm_nh, \
|
|
_FP_DIV_MEAT_1_udiv_norm_nl, \
|
|
_FP_DIV_MEAT_1_udiv_norm_y); \
|
|
R##_f = (_FP_DIV_MEAT_1_udiv_norm_q \
|
|
| (_FP_DIV_MEAT_1_udiv_norm_r != 0)); \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \
|
|
do \
|
|
{ \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl; \
|
|
_FP_W_TYPE _FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r; \
|
|
if (X##_f < Y##_f) \
|
|
{ \
|
|
R##_e--; \
|
|
_FP_DIV_MEAT_1_udiv_nl = X##_f << _FP_WFRACBITS_##fs; \
|
|
_FP_DIV_MEAT_1_udiv_nh = X##_f >> _FP_WFRACXBITS_##fs; \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_DIV_MEAT_1_udiv_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \
|
|
_FP_DIV_MEAT_1_udiv_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \
|
|
} \
|
|
udiv_qrnnd (_FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r, \
|
|
_FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl, \
|
|
Y##_f); \
|
|
R##_f = _FP_DIV_MEAT_1_udiv_q | (_FP_DIV_MEAT_1_udiv_r != 0); \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Square root algorithms:
|
|
We have just one right now, maybe Newton approximation
|
|
should be added for those machines where division is fast. */
|
|
|
|
#define _FP_SQRT_MEAT_1(R, S, T, X, q) \
|
|
do \
|
|
{ \
|
|
while ((q) != _FP_WORK_ROUND) \
|
|
{ \
|
|
T##_f = S##_f + (q); \
|
|
if (T##_f <= X##_f) \
|
|
{ \
|
|
S##_f = T##_f + (q); \
|
|
X##_f -= T##_f; \
|
|
R##_f += (q); \
|
|
} \
|
|
_FP_FRAC_SLL_1 (X, 1); \
|
|
(q) >>= 1; \
|
|
} \
|
|
if (X##_f) \
|
|
{ \
|
|
if (S##_f < X##_f) \
|
|
R##_f |= _FP_WORK_ROUND; \
|
|
R##_f |= _FP_WORK_STICKY; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* Assembly/disassembly for converting to/from integral types.
|
|
No shifting or overflow handled here. */
|
|
|
|
#define _FP_FRAC_ASSEMBLE_1(r, X, rsize) ((r) = X##_f)
|
|
#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = (r))
|
|
|
|
|
|
/* Convert FP values between word sizes. */
|
|
|
|
#define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f)
|
|
|
|
#endif /* !SOFT_FP_OP_1_H */
|